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lfunc_lfunctions • Show schema
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{'Lhash': '4362602138074636559820512830585,5651312035934587195070955083509', 'a10': -14, 'a2': 2, 'a3': 1, 'a4': 0, 'a5': -7, 'a6': 2, 'a7': -20, 'a8': -8, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6823201753278014, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -2, 4]], [7, [1, 20, 343]]], 'bad_primes': [2, 7], 'central_character': '14.1', 'coefficient_field': '1.1.1.1', 'conductor': 196, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1, -2, 4], [1, -1, -26, -27, 729], [1, 7, -76, 875, 15625], [1, 20, 343], [1, 35, -106, 46585, 1771561], [1, -132, 8750, -290004, 4826809], [1, 59, -1432, 289867, 24137569], [1, 137, 11910, 939683, 47045881], [1, -7, -12118, -85169, 148035889], [1, -212, 60014, -5170468, 594823321], [1, 75, -24166, 2234325, 887503681], [1, 11, -50532, 557183, 2565726409], [1, 996, 385846, 68645316, 4750104241], [1, -520, 226614, -41343640, 6321363049], [1, -171, -74582, 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{'__RealLiteral__': 0, 'data': '4.45809912835375765151201974082', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.17419372141557392180812905306', 'prec': 103}}
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{'algebraic': True, 'analytic_conductor': 0.6823201753278014, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 196, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 2, 1, 0, -7, 2, -20, -8, 27, -14, -35, 0, 132, -40, -7, -16, -59, 54, -137, 0, -20, -70, 7, -8, 125, 264, 80, 0, 212, -14, -75, 0, -35, -118, 140, 0, -11, -274, 132, 56, -996, -40, 520, 0, -189, 14, 171, -16, 57, 250, -59, 0, 417, 160, 245, 160, -137, 424, 17, 0, -51, -150, -540, 64, -924, -70, -439, 0, 7, 280, -1568, -216, -295, -22, 125, 0, 700, 264, 495, 112, 80, -1992, 1864, 0, 413, 1040, 212, 280, 873, -378, -2640, 0, -75, 342, 959, 0, -580, 114, -945, 0], 'euler11': [1, 35, -106, 46585, 1771561], 'euler13': [1, -132, 8750, -290004, 4826809], 'euler17': [1, 59, -1432, 289867, 24137569], 'euler19': [1, 137, 11910, 939683, 47045881], 'euler2': [1, -2, 4, 0, 0], 'euler23': [1, -7, -12118, -85169, 148035889], 'euler29': [1, -212, 60014, -5170468, 594823321], 'euler3': [1, -1, -26, -27, 729], 'euler31': [1, 75, -24166, 2234325, 887503681], 'euler37': [1, 11, -50532, 557183, 2565726409], 'euler41': [1, 996, 385846, 68645316, 4750104241], 'euler43': [1, -520, 226614, -41343640, 6321363049], 'euler47': [1, -171, -74582, -17753733, 10779215329], 'euler5': [1, 7, -76, 875, 15625], 'euler53': [1, -417, 25012, -62081709, 22164361129], 'euler59': [1, -17, -205090, -3491443, 42180533641], 'euler61': [1, 51, -224380, 11576031, 51520374361], 'euler67': [1, 439, -108042, 132034957, 90458382169], 'euler7': [1, 20, 343, 0, 0], 'euler71': [1, 1568, 1330478, 561204448, 128100283921], 'euler73': [1, 295, -301992, 114760015, 151334226289], 'euler79': [1, -495, -248014, -244054305, 243087455521], 'euler83': [1, -1864, 2012198, -1065810968, 326940373369], 'euler89': [1, -873, 57160, -615437937, 496981290961], 'euler97': [1, 580, 1909446, 529350340, 832972004929], 'euler_factors': [[1, -2, 4, 0, 0], [1, -1, -26, -27, 729], [1, 7, -76, 875, 15625], [1, 20, 343, 0, 0], [1, 35, -106, 46585, 1771561], [1, -132, 8750, -290004, 4826809], [1, 59, -1432, 289867, 24137569], [1, 137, 11910, 939683, 47045881], [1, -7, -12118, -85169, 148035889], [1, -212, 60014, -5170468, 594823321], [1, 75, -24166, 2234325, 887503681], [1, 11, -50532, 557183, 2565726409], [1, 996, 385846, 68645316, 4750104241], [1, -520, 226614, -41343640, 6321363049], [1, -171, -74582, -17753733, 10779215329], [1, -417, 25012, -62081709, 22164361129], [1, -17, -205090, -3491443, 42180533641], [1, 51, -224380, 11576031, 51520374361], [1, 439, -108042, 132034957, 90458382169], [1, 1568, 1330478, 561204448, 128100283921], [1, 295, -301992, 114760015, 151334226289], [1, -495, -248014, -244054305, 243087455521], [1, -1864, 2012198, -1065810968, 326940373369], [1, -873, 57160, -615437937, 496981290961], [1, 580, 1909446, 529350340, 832972004929]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/14/4/c/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '4-14e2-1.1-c3e2-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3], 'order_of_vanishing': 0, 'prelabel': '4-14e2-1.1-c3e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.9088601322977969, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e2-0', 'trace_hash': 1802739313247737045, 'z1': {'__RealLiteral__': 0, 'data': '3.44148627176067932895503895911', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4362602138074636559820512830585,5651312035934587195070955083509', 'Lhash_array': ['4362602138074636559820512830585', '5651312035934587195070955083509'], 'factors': ['2-14-7.4-c3-0-0', '2-14-7.2-c3-0-1'], 'label': '4-14e2-1.1-c3e2-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/14/4/c/b'}